Growth in solvable subgroups of GL_r(Z/pZ)

Let $K=Z/pZ$ and let $A$ be a subset of \GL_r(K) such that is solvable. We reduce the study of the growth of $A$ under the group operation to the nilpotent setting. Specifically we prove that either $A$ grows rapidly (meaning $|A\cdot A\cdot A|\gg |A|^{1+\delta}$), or else there are groups $U_R$ and $S$, with $S/U_R$ nilpotent such that $A_k\cap S$ is large and $U_R\subseteq A_k$, where $k$ is a bounded integer and $A_k = \{x_1 x_2...b x_k : x_i \in A \cup A^{-1} \cup {1}}$. The implied constants depend only on the rank $r$ of $\GL_r(K)$. When combined with recent work by Pyber and Szab\'o, the main result of this paper implies that it is possible to draw the same conclusions without supposing that is solvable.Comment: 46 pages. This version includes revisions recommended by an anonymous referee including, in particular, the statement of a new theorem, Theorem

Bounds on the diameter of Cayley graphs of the symmetric group

In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree n, the word length in terms of S of every permutation is bounded above by a polynomial of n. We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.Comment: 17 pages, 6 table

Indigenous uses of wild and tended plant biodiversity maintain ecosystem services in agricultural landscapes of the Terai Plains of Nepal

BACKGROUND: Despite a rapidly accumulating evidence base quantifying ecosystem services, the role of biodiversity in the maintenance of ecosystem services in shared human-nature environments is still understudied, as is how indigenous and agriculturally dependent communities perceive, use, and manage biodiversity. The present study aims to document traditional ethnobotanical knowledge of the ecosystem service benefits derived from wild and tended plants in rice-cultivated agroecosystems, compare this to botanical surveys, and analyze the extent to which ecosystem services contribute social-ecological resilience in the Terai Plains of Nepal. METHOD: Sampling was carried out in four landscapes, 22 Village District Committees, and 40 wards in the monsoon season. Data collection was based on transects walks to collect plant specimens, structured and semi-structured interviews, and participatory fieldwork in and around home gardens, farms, and production landscapes. We asked 180 farmers to free-list vernacular names and describe use-value of wild and tended plants in rice-cultivated agroecosystems. Uses were categorized into eight broad groupings, and 61 biomedical ailment classifications. We assessed if knowledge of plant species diversity and abundance differed with regard to caste, age, and gender. RESULTS: Nepalese farmers have a deep knowledge of the use and management of the 391 vascular plant specimens identified, which provide key provisioning, regulating, supporting, and cultural ecosystem services. Altogether, plants belong to 76 distinct plant species from 49 phylogenetic families: 56 are used to cure 61 ailments, 27 for rituals, 25 for food, 20 for timber, 17 for fuel, 17 for fodder, 11 for soil enhancement, and eight for pesticides. Four caste groups have statistically different knowledge, and younger informants report a lower average number of useful plants. CONCLUSION: Agricultural landscapes in Nepal are reservoirs of biodiversity. The knowledge of the use of wild and tended plant species in and around these farms differs by the caste and age group of land manager. Conducting research on agroecosystems will contribute to a deeper understanding of how nature is perceived by locals, to more efficient management and conservation of the breadbasket of Nepal, and to the conservation of valuable, but disappearing traditional knowledge and practice

On the Topology of Black Hole Event Horizons in Higher Dimensions

In four dimensions the topology of the event horizon of an asymptotically flat stationary black hole is uniquely determined to be the two-sphere $S^2$. We consider the topology of event horizons in higher dimensions. First, we reconsider Hawking's theorem and show that the integrated Ricci scalar curvature with respect to the induced metric on the event horizon is positive also in higher dimensions. Using this and Thurston's geometric types classification of three-manifolds, we find that the only possible geometric types of event horizons in five dimensions are $S^3$ and $S^2 \times S^1$. In six dimensions we use the requirement that the horizon is cobordant to a four-sphere (topological censorship), Friedman's classification of topological four-manifolds and Donaldson's results on smooth four-manifolds, and show that simply connected event horizons are homeomorphic to $S^4$ or $S^2\times S^2$. We find allowed non-simply connected event horizons $S^3\times S^1$ and $S^2\times \Sigma_g$, and event horizons with finite non-abelian first homotopy group, whose universal cover is $S^4$. Finally, following Smale's results we discuss the classification in dimensions higher than six.Comment: 12 pages, minor edits 27/09/0

Daily oral grepafloxacin vs. twice daily oral doxycycline in the treatment of Chlamydia trachomatis endocervical infection.

OBJECTIVE: To compare the efficacy and safety of a 7-day course of treatment with oral grepafloxacin, 400 mg once daily, and oral doxycycline, 100 mg twice daily, in patients with chlamydial cervicitis. METHODS: Women aged 18 years or older attending 17 sexually transmitted disease clinics in the United States who had clinical signs of mucopurulent cervicitis or who had a recent positive culture or nonculture test for Chlamydia trachomatis or who had contact with a male partner with a positive culture for C. trachomatis were enrolled into this randomized, double-blind, active-controlled clinical study. The diagnosis of chlamydial cervicitis was based on culture for C. trachomatis. Patients were randomized to receive a 7-day course of treatment with either oral grepafloxacin, 400 mg once daily, or oral doxycycline, 100 mg twice daily. Response to therapy was assessed 3-8 days and 21-28 days after completion of treatment. The primary measure of efficacy was eradication of C. trachomatis at the 21-28 day follow-up visit. Clinical success, defined as improvement or complete resolution of the signs and symptoms of cervicitis, was a secondary measure of efficacy. RESULTS: Of the 451 female patients enrolled, 228 received grepafloxacin and 223 received doxycycline. In all, 154/451 (35%) patients were evaluable at the 21-28 day follow-up (81 who received grepafloxacin and 73 who received doxycycline). Microbiologic and clinical success rates demonstrated the equivalence of the two treatments. The C. trachomatis eradication rates were 96.3% (78/81) and 98.6% (72/73) for patients receiving grepafloxacin or doxycycline, respectively. The two study drugs were also equivalent in resolving clinical signs and symptoms, with clinical success rates of 88.9% (64/72) and 89.5% (51/57) for patients treated with grepafloxacin and doxycycline, respectively. Both drugs were well tolerated, with 47% of patients receiving grepafloxacin and 46% of patients receiving doxycycline experiencing drug-related adverse events, none of which was serious. CONCLUSIONS: Seven days of treatment with oral grepafloxacin, 400 mg once daily, was as effective as 7 days of treatment with oral doxycycline, 100 mg twice daily, in patients with cervicitis caused by C. trachomatis. Both agents were well tolerated and had comparable safety profiles. Grepafloxacin's once-daily dosing regimen may offer advantages in terms of patient compliance

Twisted Open Strings from Closed Strings: The WZW Orientation Orbifolds

Including {\it world-sheet orientation-reversing automorphisms} $\hat{h}_{\sigma} \in H_-$ in the orbifold program, we construct the operator algebras and twisted KZ systems of the general WZW {\it orientation orbifold} $A_g (H_-) /H_-$. We find that the orientation-orbifold sectors corresponding to each $\hat{h}_{\sigma} \in H_-$ are {\it twisted open} WZW strings, whose properties are quite distinct from conventional open-string orientifold sectors. As simple illustrations, we also discuss the classical (high-level) limit of our construction and free-boson examples on abelian $g$.Comment: 65 pages, typos correcte

Kaluza-Klein Multi-Black Holes in Five-Dimensional Einstein-Maxwell Theory

We construct the Kaluza-Klein multi-black hole solutions on the Gibbons-Hawking multi-instanton space in the five-dimensional Einstein-Maxwell theory. We study geometric properties of the multi-black hole solutions. In particular, unlike the Gibbons-Hawking multi-instanton solutions, each nut-charge is able to take a different value due to the existence of black hole on it. The spatial cross section of each horizon can be admitted to have the topology of a different lens space L(n;1)=S^3/Z_n addition to S^3.Comment: 8 pages, to be published in Classical and Quantum Gravit

Lemierre's Syndrome Complicating Pregnancy

Lemierre's syndrome is an anaerobic suppurative thrombophlebitis involving the internal jugular vein secondary to oropharyngeal infection. There is only one previous case report in pregnancy which was complicated by premature delivery of an infant that suffered significant neurological damage. We present an atypical case diagnosed in the second trimester with a live birth at term. By reporting this case, we hope to increase the awareness of obstetricians to the possibility of Lemierre's syndrome when patients present with signs of unabating oropharyngeal infection and pulmonary symptoms

On the Gannon-Lee Singularity Theorem in Higher Dimensions

The Gannon-Lee singularity theorems give well-known restrictions on the spatial topology of singularity-free (i.e., nonspacelike geodesically complete), globally hyperbolic spacetimes. In this paper, we revisit these classic results in the light of recent developments, especially the failure in higher dimensions of a celebrated theorem by Hawking on the topology of black hole horizons. The global hyperbolicity requirement is weakened, and we expand the scope of the main results to allow for the richer variety of spatial topologies which are likely to occur in higher-dimensional spacetimes.Comment: 13 pages, no figures, to appear in Class. Quantum Gra

Expansion in SL_d(Z/qZ), q arbitrary

Let S be a fixed finite symmetric subset of SL_d(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of pi_q(G) with respect to the generating set pi_q(S) form a family of expanders, where pi_q is the projection map Z->Z/qZ